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Tutte polynomials of alternating polycyclic chains

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Abstract

The Tutte poynomial T(G; x, y) of a graph G is a two-variable graph polynomial, and it gives interesting information about the graph. Many chemically interesting polycyclic polymers can be modeled by uniform or non-uniform polycyclic graphs. In this paper, we consider the Tutte poynomial of several classes of alternating polycyclic chains which contain phenylene chains and their dicyclobutadieno derivatives as special cases. Further, explicit closed formula of the number of spanning trees, the number of spanning forests and the number of spanning connected subgraphs of phenylenes (resp. the dicyclobutadieno derivatives of phenylenes) are obtained.

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Acknowledgements

This work is partially supported by the Hunan Provincial Natural Science Foundation of China (2018JJ2249) and Hunan Provincial Innovation Foundation for Postgraduate (CX2017B170).

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Authors and Affiliations

  1. College of Computer Engineering and Applied Mathematics, Changsha University, Changsha, 410022, Hunan, China

    Hanlin Chen

  2. College of Financial Mathematics and Statistics, Guangdong University of Finance, Guangzhou, 510521, Guangdong, China

    Qiuzhi Guo

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  1. Hanlin Chen
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  2. Qiuzhi Guo
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Correspondence to Hanlin Chen.

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Chen, H., Guo, Q. Tutte polynomials of alternating polycyclic chains. J Math Chem 57, 2248–2260 (2019). https://doi.org/10.1007/s10910-019-01069-2

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  • DOI: https://doi.org/10.1007/s10910-019-01069-2

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